Experimental determination and theoretical prediction for the frequency compromise in bowed string and wind instruments

Abstract

In musical instruments, eigenfrequencies of resonators (strings, pipes) are generally not strictly harmonic. When the oscillation is sustained by means of an external nonlinearity (bow,reed) the harmonic frequencies of the vibration cannot fully coincide with these eigenfrequencies. The notion of reactive power balance brings a new insight on the frequency compromise for a given spectrum. On the violin, flattening of the pitch when the bow pressure increases may be explained and quantitatively predicted by this sumrule [X. Boutillon, J. Acoust. Soc. Am. 90, 754–763 (1991)]. Measurements of the frequency compromise (without and with flattening) will be presented on a bowed string and compared with theoretical predictions. Experimental results shed light on one aspect of the rosin friction curve between the bow and the string. The same approach is relevant on wind instruments and might give information on the reed dynamical properties. [Work supported by CNRS and French Ministry of Culture.]